In the following cross between two mulatto genotypes (AaBbCc x AaBbCc), each parent produces eight different types of gametes and these gametes combine with each other in 64 different ways resulting in a total of seven skin colors. The skin colors can be represented by the number of capital letters, ranging from zero (no capital letters) to six (all capital letters). The approximate shades of skin color corresponding to each genotype are shown in Table 1. Note: Skin color may involve at least four pairs of alleles with nine (or more) shades of skin color.

The cross in Table 1 can also be shown with the bionomial expansion (a + b)⁶ where the letter a = number of capital letters and the letter b = number of small case letters. Each term in the expression represents the number of offspring with a specific skin color phenotype based on the number of capital letters in the genotype. For example, 20 offspring have three capital letters in their genotype and have a skin color that is intermediate between very dark with all caps (AABBCC) and very light with no caps (aabbcc).

Multiple gene (polygenic) inheritance explains many plant and animal traits where there is a wide variation between extreme phenotypes, with most individuals having intermediate phenotypes. Some examples of polygenic inheritance are: human skin and eye color; height, weight and inteligence in people; and kernel color of wheat. In fact, kernel color in wheat is nicely shown in Table 2. Table 2 is essential the same as Table 1, except the extremes in color are dark red and white, rather than black and white. In polygenic inheritance the "dominant" capital genes are additive, each capital gene adding one unit of color to the genotype. With more capital genes, the phenotype (appearance) gets darker. The garden peas studied by Gregor Mendel involved pairs of alleles with only three possible genotypes and two phenotypes per trait. For example, the gene for round pea (R) is dominant over the gene for wrinkled pea (r) and only three genotypes are possible: RR, Rr and rr. These three genotypes produce only two phenotypes: Round (RR and Rr) and wrinkled (rr). There are no intermediate traits between round and wrinkled. If all human characteristics were controlled by simple pairs of dominant and recessive alleles like the one Mendel studied, we would have tall and short people with no intermediates. Polygenic inheritance is yet another exception to Mendel's genetic ratios.

In order to determine how many different genotypes are possible, you must first determine how many different gametes are possible for each parent, then match all the gametes in a genetic checkerboard (See the following Table 3). Although the three pairs of genes are linked to one homologous pair of chromosomes, there are a total of eight different possible gametes for each parent: CDE, CDe, CdE, Cde, cDE, cDe, cdE, and cde. This number of gametes is based on all the total possible ways these genes can be inherited on each chromosome of homologous pair #1. [It is not based on the random assortment of these genes during meiosis in the parents because all three genes are closely linked together on the same chromosome; therefore, all three genes tend to appear together in the same two gametes: CDE and cde.] The possible different genotypes are shown in the following Table 3: